___________________________________________________________________________ Operations Research  Jan Fábry Project Management

___________________________________________________________________________ Operations Research  Jan Fábry  Project Activity 1 Activity 2 Activity 3 Activity 4 Activity 6 Activity 7 Activity 5

Project Management ___________________________________________________________________________ Operations Research  Jan Fábry Activity 1 Activity 2 Activity 3 Activity 4 Activity 6 Activity 7 Activity 5 Activity  Node NETWORK – graphical representation of the project

Project Management ___________________________________________________________________________ Operations Research  Jan Fábry Activity  Arc NETWORK – graphical representation of the project ACT 1 ACT 11 ACT 2 ACT 3 ACT 4 ACT 5 ACT 6 ACT 7 ACT 8 ACT 9 ACT 10

___________________________________________________________________________ Operations Research  Jan Fábry  Event Activity A Design a car Activity B Make a prototype Start point of A Finish point of A Start point of B Finish point of B Project Management

___________________________________________________________________________ Operations Research  Jan Fábry Activity A Design a car Activity B Make a prototype Project Management Activity A immediately PRECEDES activity B Activity B immediately SUCCEEDS activity A

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Activity A is the predecessor of Activity B and C Activity A Design a car Activity B Make a prototype 4 Activity C Computer presentation

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Activity A Design a car Activity B Make a prototype Activity C Computer presentation 5 Activity E Prototype test Activity D Prototype presentation Dummy activity Activity E (Prototype test) follows Activity B Activity D (Prototype presentation) follows Activity B and C

___________________________________________________________________________ Operations Research  Jan Fábry Project Management - time Activity Requirements - money (cost) - machines - people - material

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Phases of Project Management Network  Planning  Controlling  Scheduling Start and finish times for each activity Finish time of project Periodic progress reports

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Methods Deterministic time Critical Path Method (CPM) Probabilistic time Program Evaluation Review Technique (PERT)

___________________________________________________________________________ Operations Research  Jan Fábry CPM Project Management

___________________________________________________________________________ Operations Research  Jan Fábry Project Management CPM  Finish time of the project  Start and finish times of each activity  A critical path consisting of critical activities  Non-critical activities and their possible delay

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Example - Music DM, Inc.  Christmas compilation of Czech carols  11 activities: 1) Songs Selection 2) Mastering 3) Promotion Material Elaborating CPM

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Example - Music DM, Inc.  11 activities: 4) Customers Analysis 5) Promotion Material Production 6) Make CD Copies 7) Customers Selection CPM

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Example - Music DM, Inc.  11 activities: 8) Data to Printing House 9) Promotion Material to Printing House 10) Laser Print 11) Mailing CPM

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Example - Music DM, Inc. Activity DescriptionDurationPredecessors A Songs Selection 15None BMastering8A C Promotion Material Elaborating 6A D Customers Analysis 7A E Promotion Material Production 4 C, D F Promotion Material to PH 5E G Customers Selection 3D CPM

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Example - Music DM, Inc. Activity DescriptionDurationPredecessors H Make CD Copies 12 B, D I Data to PH 3G J Laser Print 9 F, I KMailing8 H, J  All the envelopes have to be delivered until December 12  Objective: set the starting date of the project CPM

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Example - Music DM, Inc. Solution - CPM 1) Construct the network 2) Event analysis - forward pass - backward pass 3) Activity analysis - critical activities - noncritical activities CPM

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Example - Music DM, Inc. 1) Construct the network One start node & one end node Each activity  one arc Two nodes are connected maximally by one arc CPM

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Example - Music DM, Inc. 1) Construct the network i j i < j CPM

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Example - Music DM, Inc. Activity DescriptionDurationPredecessors A Songs Selection 15None BMastering8A C Promotion Material Elaborating 6A D Customers Analysis 7A E Promotion Material Production 4 C, D F Promotion Material to PH 5E G Customers Selection 3D CPM

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Example - Music DM, Inc. Activity DescriptionDurationPredecessors H Make CD Copies 12 B, D I Data to PH 3G J Laser Print 9 F, I KMailing8 H, J CPM

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Example - Music DM, Inc A B D C D1D1 E FH D2D2 GI J KCPM

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Example - Music DM, Inc CPM

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Example - Music DM, Inc. 2) Event analysis - forward pass The earliest event time for a node is the earliest time at which all the preceding activities have been completed. j ET j CPM

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Example - Music DM, Inc. 2) Event analysis - forward pass ET 1 ET 1  ET 2 ET 2  ET 3 ET 3 …  ET n Ascending order: The earliest event time for completing a project is the earliest time of the last event. T = ET n CPM

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Example - Music DM, Inc. 2) Event analysis - backward pass The latest event time for a node is the latest time at which the event can occur without delaying the determined completion time of the project. i LT i CPM

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Example - Music DM, Inc. 2) Event analysis - backward pass LT 1  LT 2  LT 3  …  LT n Descending order: The latest event time for completing a project can be set in the planning process or can be considered as the earliest event time for completing a project. LT n = T = ET n or LT n = T PL > T CPM

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Example - Music DM, Inc. 3) Activity analysis Total float: i LT i ET i j ET j LT j t ij CPM

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Example - Music DM, Inc. 3) Activity analysis Critical activity: TF ij = 0 TF ij = T PL - T if LT n = T = ET n if LT n = T = ET n if LT n = T PL > T if LT n = T PL > T Noncritical activity: TF ij > 0 TF ij > T PL - T if LT n = T = ET n if LT n = T = ET n if LT n = T PL > T if LT n = T PL > T CPM

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Example - Music DM, Inc. 3) Activity analysis Critical path: A B D C D1D1 E F H D2D2 GI J KCPM

___________________________________________________________________________ Operations Research  Jan Fábry Project Management Example - Music DM, Inc. 3) Activity analysis Noncritical activity 1) Start of the activity can be postponed 2) Duration of the activity can be extended 3) Combination of 1 and 2 CPM